The existing analytical solutions are extended to obtain the stress fields and the stress intensity factors(SIFs) of two unequal aligned cracks emanating from an elliptical hole in an infinite isotropic plane. A confo...The existing analytical solutions are extended to obtain the stress fields and the stress intensity factors(SIFs) of two unequal aligned cracks emanating from an elliptical hole in an infinite isotropic plane. A conformal mapping is proposed and combined with the complex variable method. Due to some difficulties in the calculation of the stress function, the mapping function is approximated and simplified via the applications of the series expansion. To validate the obtained solution, several examples are analyzed with the proposed method, the finite element method, etc. In addition, the effects of the lengths of the cracks and the ratio of the semi-axes of the elliptical hole(a/b) on the SIFs are studied. The results show that the present analytical solution is applicable to the SIFs for small cracks.展开更多
The three-dimensional finite element method is used to solve the problem of the quarter-elliptical comer crack of the bolt-hole in mechanical joints being subjected to remote tension. The square-root stress singularit...The three-dimensional finite element method is used to solve the problem of the quarter-elliptical comer crack of the bolt-hole in mechanical joints being subjected to remote tension. The square-root stress singularity around the corner crack front is simulated using the collapsed 20-node quarter point singular elements. The contact interaction between the bolt and the hole boundary is considered in the finite element analysis. The stress intensity factors （SIFs） along the crack front are evaluated by using the displacement correlation technique. The effects of the amount of clearance between the hole and the bolt on the SIFs are investigated. The numerical results indicate that the SIF for mode I decrease with the decreases in clearance, and in the cases of clearance being present, the corner crack is in a mix-mode, even if mode I loading is dominant.展开更多
The hatches for inspecting are usually designed with elliptical holes in airplane structures, so computation of the stress intensity factor of three dimensional crack at elliptical holes is pivotal for damage toleranc...The hatches for inspecting are usually designed with elliptical holes in airplane structures, so computation of the stress intensity factor of three dimensional crack at elliptical holes is pivotal for damage tolerance analysis of these structures. In this paper, weight function is derived for a two dimensional through cracks at elliptical holes by applying a compounding method. Stress intensity factor formulas for an internal surface semi-elliptical crack in elliptical holes are obtained wing the three dimensional weight function method. Stress intensity factors for an internal surface semi-elliptical crack in elliptical holes under remote tension are computed. At the same time, research on how radius of curvature for elliptical holes affect stress intensity factors was conducted. Stress intensity factors decrease when radius of curvature increases. Some results and conclusions which are of practical value are given.展开更多
The solution of surface displacement of an elliptical crack under compressive-shear loading was obtained by using the complex function method. The closing mode was established by analyzing the geometrical condition of...The solution of surface displacement of an elliptical crack under compressive-shear loading was obtained by using the complex function method. The closing mode was established by analyzing the geometrical condition of closing crack, and the corresponding critical stress was solved. The result corrects the traditional viewpoint, in which there exist only open or close states for an elliptical crack, and points out that the local closing is also one of crack states. Based on them, the effect of the closed crack on stress intensity factor was discussed in detail, and its rational formulae are put forward.展开更多
Initiation and propagation of cracks in rotating disks may cause catastrophic failures. Therefore, determination of fracture parameters under different working con- ditions is an essential issue. In this paper, a comp...Initiation and propagation of cracks in rotating disks may cause catastrophic failures. Therefore, determination of fracture parameters under different working con- ditions is an essential issue. In this paper, a comprehensive study of stress intensity factors （SIFs） in rotating disks containing three-dimensional （3D） semi-elliptical cracks subjected to different working conditions is carried out. The effects of mechanical prop- erties, rotational velocity, and orientation of cracks on SIFs in rotating disks under cen- trifugal loading are investigated. Also, the effects of using composite patches to reduce SIFs in rotating disks are studied. The effects of patching design variables such as mechanical properties, thickness, and ply angle are investigated separately. The modeling and analytical procedure are verified in comparison with previously reported results in the literature.展开更多
The method of complex function and the method of Green's function are used to investigate the problem of SH-wave scattering by radial cracks of any limited length along the radius originating at the boundary of an...The method of complex function and the method of Green's function are used to investigate the problem of SH-wave scattering by radial cracks of any limited length along the radius originating at the boundary of an elliptical hole, and the solution of dynamic stress intensity factor at the crack tip was given. A Green's function was constructed for the problem, which is a basic solution of displacement field for an elastic half space containing a half elliptical gap impacted by anti-plane harmonic linear source force at any point of its horizontal boundary. With division of a crack technique, a series of integral equations can be established on the conditions of continuity and the solution of dynamic stress intensity factor can be obtained. The influence of an elliptical hole on the dynamic stress intensity factor at the crack tip was discussed.展开更多
In this paper, Muskhelishvili complex function theory and boundary collocation method are used to calculate the stress intensity factors (SIF) of a plate with two cracks emanating from an arbitrary hole. The calculate...In this paper, Muskhelishvili complex function theory and boundary collocation method are used to calculate the stress intensity factors (SIF) of a plate with two cracks emanating from an arbitrary hole. The calculated examples include a circular, elliptical, rectangular, or rhombic hole in a plate. The principle and procedure by the method is not only rather simple, but also has good accuracy. The SIF values calculated compare very favorably with the existing solutions. A t the same time,the method can be used far different finite plate with two cracks emanating from a hole with more complex geometrical and loading conditions. It is an effective unified approach for this kind of fracture problems.展开更多
This paper presents a formulation for three-dimensional elasto-dynamics with an elliptic crack based on the Laplace and Fourier transforms and the convolution theorem. The dynamic stress intensity factor for the crack...This paper presents a formulation for three-dimensional elasto-dynamics with an elliptic crack based on the Laplace and Fourier transforms and the convolution theorem. The dynamic stress intensity factor for the crack is determined by solving a Fredholm integral equation of the first kind. The results of this paper are very close to those given by the two-dimensional dual integral equation method.展开更多
Through detailed three-dimensional （3D） finite element （FE） calculations, the out-of-plane constraints Tz along embedded center-elliptical cracks in mode I elastic plates are studied. The distributions of Tz are o...Through detailed three-dimensional （3D） finite element （FE） calculations, the out-of-plane constraints Tz along embedded center-elliptical cracks in mode I elastic plates are studied. The distributions of Tz are obtained near the crack front with aspect ratios （a/c） of 0.2, 0.4, 0.5, 0.6, 0.8 and 1.0. Tz decreases from an approximate value of Poisson ratio v at the crack tip to zero with increasing normalized radial distances （r/a） in the normal plane of the crack front line, and increases gradually when the elliptical parameter angle φ changes from 0° to 90°at the same r/a. With a/c rising to 1.0, Tz is getting nearly independent of φ and is only related to r/a. Based on the present FE calculations for Tz, empirical formulas for Tz are obtained to describe the 3D distribution of Tz for embedded center-elliptical cracks using the least squares method in the range of 0.2 ≤ a/c ≤ 1.0. These Tz results together with the corresponding stress intensity factor K are well suitable for the analysis of the 3D embedded centerelliptical crack from field, and a two-parameter K-Tz principle is proposed.展开更多
Using the complex variable function method and the technique of conformal mapping, the anti-plane shear problem of an elliptic hole with asymmetric colfinear cracks in a one-dimensional hexagonal quasi-crystal is solv...Using the complex variable function method and the technique of conformal mapping, the anti-plane shear problem of an elliptic hole with asymmetric colfinear cracks in a one-dimensional hexagonal quasi-crystal is solved, and the exact analytic solutions of the stress intensity factors （SIFs） for mode Ⅲ problem are obtained. Under the limiting conditions, the present results reduce to the Griffith crack and many new results obtained as well, such as the circular hole with asymmetric collinear cracks, the elliptic hole with a straight crack, the mode T crack, the cross crack and so on. As far as the phonon field is concerned, these results, which play an important role in many practical and theoretical applications, are shown to be in good agreement with the classical results.展开更多
It is a common phenomenon that the cracks originating from a hole can cause structural damage in engineering.However,the fracture mechanics studies of hole edge crack problems are not sufficient.The problem of an elli...It is a common phenomenon that the cracks originating from a hole can cause structural damage in engineering.However,the fracture mechanics studies of hole edge crack problems are not sufficient.The problem of an elliptical hole with two collinear edge cracks of unequal length in an infinite plate under uniform tension at infinity is investigated.Based on the complex variable method,the analytical solutions of stress functions and stress intensity factors are provided.The stress distribution along the axes and the edge of the elliptical hole is given graphically.The numerical results show that there is obvious stress concentration near the hole and cracks,and the stresses tend to applied loads at distances far from the defect,which conform to Saint-Venant’s principle.Hence,the stress functions are proved to be right.Under special conditions,the present configuration becomes the Griffith crack,two symmetrical cracks emanating from an elliptical hole,two cracks of unequal length emanating from a circular hole,a crack at the edge of a circular hole,or a crack emanating from an elliptical hole.Compared with available results,stress intensity factors for these special shapes of ellipses and cracks show good coincidence.The stress intensity factor for two cracks of unequal length at the edge of an elliptical hole increases with the crack length and the major-to-minor axis ratio of the elliptical hole.The stress distribution in an infinite plate containing an elliptic hole with unsymmetrical cracks is given for the first time.展开更多
The complex variable method for solving the two-dimensional thermal stress problem of icosahedral quasicrystals is stated. The closed-form solutions for icosahedral quasicrystals containing an elliptical hole subjecte...The complex variable method for solving the two-dimensional thermal stress problem of icosahedral quasicrystals is stated. The closed-form solutions for icosahedral quasicrystals containing an elliptical hole subjected to a remote uniform heat flow are obtained. When the hole degenerates into a crack, the explicit solutions for the stress intensity factors is presented.展开更多
文摘The existing analytical solutions are extended to obtain the stress fields and the stress intensity factors(SIFs) of two unequal aligned cracks emanating from an elliptical hole in an infinite isotropic plane. A conformal mapping is proposed and combined with the complex variable method. Due to some difficulties in the calculation of the stress function, the mapping function is approximated and simplified via the applications of the series expansion. To validate the obtained solution, several examples are analyzed with the proposed method, the finite element method, etc. In addition, the effects of the lengths of the cracks and the ratio of the semi-axes of the elliptical hole(a/b) on the SIFs are studied. The results show that the present analytical solution is applicable to the SIFs for small cracks.
基金National Natural Science Foundation of China (10272036)
文摘The three-dimensional finite element method is used to solve the problem of the quarter-elliptical comer crack of the bolt-hole in mechanical joints being subjected to remote tension. The square-root stress singularity around the corner crack front is simulated using the collapsed 20-node quarter point singular elements. The contact interaction between the bolt and the hole boundary is considered in the finite element analysis. The stress intensity factors （SIFs） along the crack front are evaluated by using the displacement correlation technique. The effects of the amount of clearance between the hole and the bolt on the SIFs are investigated. The numerical results indicate that the SIF for mode I decrease with the decreases in clearance, and in the cases of clearance being present, the corner crack is in a mix-mode, even if mode I loading is dominant.
文摘The hatches for inspecting are usually designed with elliptical holes in airplane structures, so computation of the stress intensity factor of three dimensional crack at elliptical holes is pivotal for damage tolerance analysis of these structures. In this paper, weight function is derived for a two dimensional through cracks at elliptical holes by applying a compounding method. Stress intensity factor formulas for an internal surface semi-elliptical crack in elliptical holes are obtained wing the three dimensional weight function method. Stress intensity factors for an internal surface semi-elliptical crack in elliptical holes under remote tension are computed. At the same time, research on how radius of curvature for elliptical holes affect stress intensity factors was conducted. Stress intensity factors decrease when radius of curvature increases. Some results and conclusions which are of practical value are given.
文摘The solution of surface displacement of an elliptical crack under compressive-shear loading was obtained by using the complex function method. The closing mode was established by analyzing the geometrical condition of closing crack, and the corresponding critical stress was solved. The result corrects the traditional viewpoint, in which there exist only open or close states for an elliptical crack, and points out that the local closing is also one of crack states. Based on them, the effect of the closed crack on stress intensity factor was discussed in detail, and its rational formulae are put forward.
文摘Initiation and propagation of cracks in rotating disks may cause catastrophic failures. Therefore, determination of fracture parameters under different working con- ditions is an essential issue. In this paper, a comprehensive study of stress intensity factors （SIFs） in rotating disks containing three-dimensional （3D） semi-elliptical cracks subjected to different working conditions is carried out. The effects of mechanical prop- erties, rotational velocity, and orientation of cracks on SIFs in rotating disks under cen- trifugal loading are investigated. Also, the effects of using composite patches to reduce SIFs in rotating disks are studied. The effects of patching design variables such as mechanical properties, thickness, and ply angle are investigated separately. The modeling and analytical procedure are verified in comparison with previously reported results in the literature.
文摘The method of complex function and the method of Green's function are used to investigate the problem of SH-wave scattering by radial cracks of any limited length along the radius originating at the boundary of an elliptical hole, and the solution of dynamic stress intensity factor at the crack tip was given. A Green's function was constructed for the problem, which is a basic solution of displacement field for an elastic half space containing a half elliptical gap impacted by anti-plane harmonic linear source force at any point of its horizontal boundary. With division of a crack technique, a series of integral equations can be established on the conditions of continuity and the solution of dynamic stress intensity factor can be obtained. The influence of an elliptical hole on the dynamic stress intensity factor at the crack tip was discussed.
文摘In this paper, Muskhelishvili complex function theory and boundary collocation method are used to calculate the stress intensity factors (SIF) of a plate with two cracks emanating from an arbitrary hole. The calculated examples include a circular, elliptical, rectangular, or rhombic hole in a plate. The principle and procedure by the method is not only rather simple, but also has good accuracy. The SIF values calculated compare very favorably with the existing solutions. A t the same time,the method can be used far different finite plate with two cracks emanating from a hole with more complex geometrical and loading conditions. It is an effective unified approach for this kind of fracture problems.
基金The project supported by the National Natural Science Foundation of China (K19672007)
文摘This paper presents a formulation for three-dimensional elasto-dynamics with an elliptic crack based on the Laplace and Fourier transforms and the convolution theorem. The dynamic stress intensity factor for the crack is determined by solving a Fredholm integral equation of the first kind. The results of this paper are very close to those given by the two-dimensional dual integral equation method.
基金The project supported by the National Natural Science Foundation of China （50275073）
文摘Through detailed three-dimensional （3D） finite element （FE） calculations, the out-of-plane constraints Tz along embedded center-elliptical cracks in mode I elastic plates are studied. The distributions of Tz are obtained near the crack front with aspect ratios （a/c） of 0.2, 0.4, 0.5, 0.6, 0.8 and 1.0. Tz decreases from an approximate value of Poisson ratio v at the crack tip to zero with increasing normalized radial distances （r/a） in the normal plane of the crack front line, and increases gradually when the elliptical parameter angle φ changes from 0° to 90°at the same r/a. With a/c rising to 1.0, Tz is getting nearly independent of φ and is only related to r/a. Based on the present FE calculations for Tz, empirical formulas for Tz are obtained to describe the 3D distribution of Tz for embedded center-elliptical cracks using the least squares method in the range of 0.2 ≤ a/c ≤ 1.0. These Tz results together with the corresponding stress intensity factor K are well suitable for the analysis of the 3D embedded centerelliptical crack from field, and a two-parameter K-Tz principle is proposed.
基金supported by the National Natural Science Foundation of China (Grant No 10761005)the Inner Mongolia Natural Science Foundation of China (Grant No 200607010104)
文摘Using the complex variable function method and the technique of conformal mapping, the anti-plane shear problem of an elliptic hole with asymmetric colfinear cracks in a one-dimensional hexagonal quasi-crystal is solved, and the exact analytic solutions of the stress intensity factors （SIFs） for mode Ⅲ problem are obtained. Under the limiting conditions, the present results reduce to the Griffith crack and many new results obtained as well, such as the circular hole with asymmetric collinear cracks, the elliptic hole with a straight crack, the mode T crack, the cross crack and so on. As far as the phonon field is concerned, these results, which play an important role in many practical and theoretical applications, are shown to be in good agreement with the classical results.
基金Supported by Hebei Provincial Natural Science Foundation of China(Grant No.A2011210033)Foundation of Hebei Education Department of China(Grant No.ZH2011116)
文摘It is a common phenomenon that the cracks originating from a hole can cause structural damage in engineering.However,the fracture mechanics studies of hole edge crack problems are not sufficient.The problem of an elliptical hole with two collinear edge cracks of unequal length in an infinite plate under uniform tension at infinity is investigated.Based on the complex variable method,the analytical solutions of stress functions and stress intensity factors are provided.The stress distribution along the axes and the edge of the elliptical hole is given graphically.The numerical results show that there is obvious stress concentration near the hole and cracks,and the stresses tend to applied loads at distances far from the defect,which conform to Saint-Venant’s principle.Hence,the stress functions are proved to be right.Under special conditions,the present configuration becomes the Griffith crack,two symmetrical cracks emanating from an elliptical hole,two cracks of unequal length emanating from a circular hole,a crack at the edge of a circular hole,or a crack emanating from an elliptical hole.Compared with available results,stress intensity factors for these special shapes of ellipses and cracks show good coincidence.The stress intensity factor for two cracks of unequal length at the edge of an elliptical hole increases with the crack length and the major-to-minor axis ratio of the elliptical hole.The stress distribution in an infinite plate containing an elliptic hole with unsymmetrical cracks is given for the first time.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11072104,11272053,and 11262017)the Key Project of Chinese Ministry of Education(Grant No.212029)+3 种基金the Natural Science Foundation of Inner Mongolia Autonomous Region,China(Grant No.2013MS0114)the Natural Science Foundation of Inner Mongolia Department of Public Education,China(Grant No.NJZZ13037)the Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region,China(Grant No.NJYT-13-B07)the Program for Higher-Level Talents of Inner Mongolia University,China(Grant No.125125)
文摘The complex variable method for solving the two-dimensional thermal stress problem of icosahedral quasicrystals is stated. The closed-form solutions for icosahedral quasicrystals containing an elliptical hole subjected to a remote uniform heat flow are obtained. When the hole degenerates into a crack, the explicit solutions for the stress intensity factors is presented.
